Question: Let (xi , yi) for i = 1, . . . , k + 1, denote k + 1 given points in the xy-plane such

Let (xi , yi) for i = 1, . . . , k + 1, denote k + 1 given points in the xy-plane such that no two of these points have the same x-coordinate. Show that there is a unique polynomial having the form y = β0 + β1x + . . . + βkxk that passes through these k + 1 points.

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